For obtaining, for instance, the desired quality of a manufactured produce in a manufacturing process with the best economy or otherwise monitoring an industrial process or industrial application, it is necessary to control the processes as efficiently and optimally as possible. A manufacturing process includes many important variable quantities (here only referred to as variables), the values of which are affected by the variations of the variables during the course of the process. The optimum result is achieved if the process-monitoring operator or the process-monitoring member is able to handle and control all the process-influencing variables in one and the same operation.
A conventional method of optimizing a process is to consider one variable at a time only, one-dimensional optimization. All the variables are fixed except one, whereupon the non-fixed variable is adjusted to an optimum result. Thereafter, the free variable is fixed and one of the other variables adjusted, and so on.
When the process variables have been set in this way one by one, it is supposed that the best working point of the process has been obtained. However, the fact is that this is not the whole truth. The process may still be far from its optimum working point, since the method does not take the mutual influence of the process variables into account. The difficulty of this method is to obtain a total overview of the process based on a number of mutually independent process variables as necessitated by such a view. It is only when the relationship between these variables can be interpreted correctly that the process operator gets a real overview and understanding of the process.
An operator is limited by his or her human ability to understand and control only a limited number of variables per unit of time. A process monitoring system measures up to hundreds of variables, of which perhaps some 20 more or less directly control the process. Such a monitoring system requires a computer which can continuously register if and when slight variations occur in any of the variables.
A model of a process is realized substantially by two different types of modelling techniques, mechanistic and empirical modelling. Mechanistic models are used, for example, in physics. Data are used to discard or verify the mechanistic model. A good mechanistic model has the advantage of being based on established theories and is usually very reliable over a wide range. However, the mechanistic model has its limitations and is only applicable for relatively small, simple systems, whereas it is insufficient, if even possible to use, for building an axiom around a complex industrial process. Many attempts have been made to model processes with the aid of mechanistic models based on differential equations. An important disadvantage of these models, however, is that they are greatly dependent on the dependence of certain parameters on each other. Such parameters with great dependence on each other must be determined for the model to function. In the majority of cases it is very difficult to quantify them in a reliable manner. A consequence of this is that it is very difficult to obtain mechanistic models that work in practice.
In empirical modelling the model is based on real data, which, of course, requires good-quality data. Process data consist of many different measured values. In other words, process data are multivariate, which presupposes multivariate techniques for process data to be modelled and illustrated. Different statistical methods exist for multivariate modelling. Traditional multivariate modelling technique, as for example multiple linear regression (MLR), assume independent and error-free data. For that reason, such technique cannot handle process data, since they are highly interdependent and, in addition, influenced by noise.
A solution to the above problems is to use projection technique. This technique is capable of selecting the actual variation in data and expressing this information in so-called latent (underlying) variables. The technique is described in ABB Review April, 1993, Bert Skagerberg, Lasse Sundin. The projection technique is most advantageous for obtaining a fast overview of a complex process. The two projection techniques, PCA and PLS, that is, Principal Component Analysis and Projection to Latent Structures, are tailor-made for solving problems such as process overview and identification of relationships between different process variables.
Models created with these two methods can be executed directly (on-line) in the process information system and can be used for process monitoring. PLS is highly suitable for predicting various quality-related variables, which are normally difficult to measure or sometimes even impossible to measure routinely since they occur late in the process.
Modelling by means of projection techniques (PCA, PLS) is best explained by the use of simple geometry in the form of points, lines and planes. Process data are usually listed in the form of tables, wherein a row represents a set of observations, that is, registration of variable values, in the process at a certain time. For practical reasons, and for the sake of clarity, the description will be restricted in the following to a data table with three variables, that is, three columns, which can be illustrated geometrically with the aid of a three-dimensional coordinate system (FIG. 1), where the variables in the process are represented by the axes in the coordinate system. However, the method functions for an arbitrary number of variables, K, where K&gt;3, e.g. K=50 or K=497. An observation of the relevant variables in the process at a certain time may here be represented by a point in the coordinate system which is common to all variables, which means that the measured value of each variable corresponds to a coordinate for the respective axis. Mathematically, independently of the number of coordinates, a row in the table still corresponds to a point. All n rows in the table then correspond to a swarm of points (FIG. 2). The mathematical procedure for describing a process with K relevant variables is handled in the same way by the observations at each time being represented by a point in a multidimensional room with K coordinates.
The projection method works on the assumption that two points that lie close together are also closely related in the process.
The data set may now be projected to latent variables in a series of simple geometrical operations as follows:
The midpoint in the data set is calculated. This calculated point is called x. The midpoint coordinates correspond to the mean value of all the variables in the system (FIG. 3), PA1 Starting from the midpoint x, a first straight line, p1, is drawn, which is adapted to the data set such that the distance to the line for the individual points is as small as possible. This line corresponds to the direction in the data set which explains the greatest variation in the process, that is, the dominating direction in the data set and is referred to as the first principal direction. The direction coefficients of this line are combined in the loading vector p1. Each point in the data set is then projected orthogonally to this line. The coordinates from the projection of all the points to the line form a new vector t.sub.1. (Each point gives a value, here called "score", as a component in the vector t.sub.1.) PA1 The new vector (t.sub.1) is usually called score vector and describes the first latent variable. This latent variable expresses the most important direction in the data set and is a linear combination of all three variables (or in a multi-dimensional system all K variables involved). Each variable has an influence on the latent variable which is proportional to the size of the direction coefficient in the loading vector p.sub.1. PA1 Even if the line, the first principal direction, P1, given by the loading vector, p.sub.1, according to the above is one that most closely agrees to the data set, it can still be seen from FIG. 4 that the deviations from the line are relatively large. A second line, p2, may be adapted to the point swarm which represents data in the process. This second line, p2, is orthogonal to the first line, p1, and describes the next most important direction in the point swarm (FIG. 4) and is referred to as the second principal direction. The score vector t.sub.2 and the direction coefficient p.sub.2 are interpreted analogously to t.sub.1 and p1. PA1 Overview or a quantity of data PA1 Classification (e.g. if the process continues normally or if it deviates) PA1 Real-time monitoring (e.g. to track the process conditions and discover an incipient deviation as early as possible).
Analogously, a third projection line can be constructed with the direction p.sub.3 and the score vector t.sub.3. However, the value of computing a third principal component in this three-dimensional example is limited, since the resulting three latent variables t.sub.1, t.sub.2 and t.sub.3 only represent a rotated version of the three-dimensional coordinate system.
If, instead, a look is taken at the projection plane which is defined by the first two principal directions, p.sub.1 and p.sub.2, it can be determined that this plane describes the point swarm well in two dimensions only. The advantage of this is that points projected onto a plane reproduce information which emanates from variables in three dimensions. This is one of the reasons for using PCA to analyze a complex data structure. From a number of variables a small number of underlying latent variables may be obtained, these latent variables describing the main part of the systematic information about current process data. From experience, it has proved that more than 2-6 latent variables are not required. This can also be shown theoretically. The latent variables provide an overview of the data set and can be presented in the form of different types of diagrams or graphic images. Part of the variation of the data set will remain after the latent variables have been extracted and are called residuals (deviations). These contain no systematic information and may therefore be regarded as superfluous and are often referred to as noise.
According to one approach, the projection plane, defined by the lines p.sub.1 and p.sub.2, may be seen as a two-dimensional window into the multidimensional (in the example the three-dimensional) world. The basic idea behind PCA is to construct such a projection window, providing the viewer with a picture of the multidimensional data set. Consequently, PCA ensures the best possible window, that which contains the optimum picture of the data set. Further, the window can be saved and displayed graphically. The projection window visualized on a computer screen provides an operator, for example, with an overview of a complex process.
The projections described above are essentially a geometrical interpretation of the principal component analyses which have proved to be very suitable for obtaining an overview of process data. Normally, it is sufficient also among hundreds of variables to calculate about three principal components to describe the principal information in the data set. Typical of the PCA method, when applied to process data, is that the system easily selects a strong first component, a less important second component, and a third component describing little but systematic information.
The PCA method is suitable to use for analyzing blocks of process data. Questions which may be answered in an industrial process by means of PCA are:
Another important problem is to identify relationships between process data, X, and more quality-related data, Y. This type of relationships are difficult to analyze, if even possible using traditional modelling techniques, since the relationships are often hidden in complex interactions and correlation patterns involving different process variables.
Projection to latent structures, PLS, is a projection technique which offers a method of modelling complex relationships in a process. PLS decomposes two blocks of data, X and Y, into principal components as projections (FIG. 5). The two modelled blocks are similar to the solution according to the PCA method, but differ in that in PLS the projection is made to explain X and Y simultaneously for the purpose of obtaining the best possible correlation between X and Y. Thus, the PLS method serves to model the X block in such a way that a model is obtained which in the best way predicts the Y block. A PLS model can thus be very useful for predicting quality-related parameters, which are otherwise both expensive and difficult to measure. Instead of having to wait perhaps a week before a critical value from the quality control laboratory becomes available, this value can be immediately predicted in a model. FIG. 6 illustrates an example of how the study and monitoring of an industrial process can be visualized by means of a computer screen on-line. The left half of the figure shows a score plot, that is, a representation of the observations of the measured data of the process from two latent variables t.sub.a and t.sub.b reproduced with two principal directions p.sub.a and p.sub.b as axes in the coordinate system of the graph. The left half of the picture shows both a static and a movable picture. The static picture consists of points which describe the variation in the reference data which are used for building the model. If these reference data are chosen in the best way, the picture consists of good working ranges for the process as well as ranges which should be avoided in the process. The picture may be compared to a map containing information as to which conditions the operator should strive to direct the process to, and which conditions should be avoided.
On-line execution of measured process data results in calculated markings, that is, that observations made at a new time are reproduced as a new point in the plane which is represented by that plane which, in the form of the two selected principal directions p.sub.a and p.sub.b, constitute the coordinates of the graph on the screen. This means that each new point contains information about all the relevant measured data because of the projection to the latent variables according to the PLS method. Changes in the process may then be reproduced on-line on the screen in the form of a line in the left half of the VDU. The changes are reproduced with the aid of a movable figure in the form of a curve which connects the observations at different times. The curve will thus move in time over the screen like a crawling "snake". To make the operator better understand the significance of the information provided by the crawling snake, the snake may be divided into a head and a tail, which are also illustrated in different colours and symbols. The head consists of present observations, whereas the tail is built up of "historical" observations. If an alarm is raised, that is, when the curve (the snake) detects "prohibited" areas, the snake may change colour, for example to red.
The movable curve is an aid to the operator to continuously monitor the status of the process by viewing the process through a "window" on the screen into the multivariate rooms of the process. The location of the snake's head is compared with the area where reference data of high quality have been attained. The ambition of the operator or the monitoring member of the process should be to control the process to this area.
To the right in FIG. 6 there is shown an example of other information which it may be imparted to the operator via the screen with the aid of the PLS method. The right picture is a reproduction of loading vectors, a loading plot. This is a map of how the score plot, that is, the curve in the left picture, is influenced by the individual variables in the process. The left and right picture halves also contain associated information. This means that the direction in the left picture has a direct correspondence in the right picture. The operator may receive guidance from the right picture if he/she is to control individual process variables for the purpose of moving the process (the "snake") to achieve better operating conditions for the process.
The use of the method described above means a powerful instrument in monitoring processes which are dependent on a large quantity of process variables in a simple and clear way. As examples of technical fields, within which process monitoring of industrial processes according to the described methods may advantageously be utilized, may be mentioned the pulp, paper, chemical, food, pharmaceutical, cement and petrochemical industries as well as power generation, power and heat distribution, and a wide range of other applications. However, the PCA and PLS methods, respectively, used according to the prior art suffer from a weakness in that the projection plane which built up of two principal directions, and to which plane observations are projected, are fixed and do not change during the course of the process. This means that changes in the swarm of points in the multidimensional space, which has constituted the base of the calculation of the principal directions p.sub.a and p.sub.b, are not taken into account. At the same time new observation series are constantly added during the process, in which variable values may be changed, which means that the geometry of the point swarm in space may be changed and that the calculated principal directions which are intended to reflect the shape of the point swarm are no longer of interest. This is not reflected by the graphically reproduced information about the course of the process according to the above.